A052728 A simple context-free grammar in a labeled universe.

0, 0, 2, 12, 168, 2880, 64080, 1723680, 54633600, 1992936960, 82261267200, 3790579161600, 192895381324800, 10744251136819200, 650181362358528000, 42476922345521664000, 2979716339168464896000, 223385082959833546752000

Offset: 0

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 684

Programs

Maple

spec := [S,{B=Union(S,Z,C),S=Prod(B,B),C=Prod(S,Z)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

Formula

E.g.f.: (1/2)/(x^2+1+2*x)*(1-2*x-2*x^2-(1-4*x-4*x^2)^(1/2))

Recurrence: {a(1)=0, a(2)=2, a(3)=12, (-4*n^3-16*n^2-20*n-8)*a(n) +(-8*n^2-26*n-20)*a(n+1) +(-2-3*n)*a(n+2) +a(n+3) =0.

a(n) = n!*A052705(n). - R. J. Mathar, Oct 18 2013